McConnell has voiced confidence that Republicans will nominate "electable" candidates as they seek to grow their narrow majority during an election cycle in which Democrats will be defending 23 seats to just eight for the GOP.

The majority leader is signaling to conservative groups that he'll play a big role in determining whom Republicans nominate to take on vulnerable Democrats in states from Florida to Montana.

"We intend to play in primaries if there's a clear choice between someone who can win in November and someone who can't," McConnell said at an April 7 press conference.

Conservative groups that have frequently clashed with McConnell and the GOP establishment say they intend to back candidates that could move the party to the right.

"We're looking for viable conservative candidates, and our supporters don't care whether the GOP establishment ultimately supports them or not," said Ken Cuccinelli, president of the Senate Conservatives Fund, which is backing Ohio Treasurer Josh Mandel as the Republican candidate against Sen. Sherrod Brown (D).

"Sometimes the establishment comes around to support our candidates, and sometimes they don't. But our criteria won't change."

Republicans' hopes of winning the Senate majority in 2010 and 2012 were thwarted in part by some weak candidates who defeated rivals from the GOP establishment in party primaries.

In 2014, McConnell, asked about Tea Party challengers, declared to The New York Times that "we are going to crush them everywhere."

The GOP largely did in that cycle, winning back the Senate after Sens. Thad Cochran (R-Miss.) and Pat Roberts (R-Kan.) defeated conservative challengers, and GOP leaders helped clear the field for Sen. Cory Gardner (R) to take on Democrat Mark Udall in Colorado.

"The idea, I always remind people, is to win the election, and frequently, the primary in 2010 and 2012 dictated the outcome in November," McConnell said at his press conference earlier this month.

"We didn't let that happen again in 2014 and we came to the majority. We only had one episode in 2016, in Indiana," he added, referring to the primary between conservative Rep. Marlin Stutzman (R), whom the Club for Growth backed, and Rep. Todd Young (R), whom the establishment backed.

Young won the primary and a competitive election in the fall against former Sen. Evan Bayh (D).

"We nominated the right candidate, and he won," McConnell said.

BuzzFeed reported earlier this year that a senior White House adviser told donors that "the days of McConnell picking Republican nominees in Senate races is over."

But the White House later pushed back against the report, and McConnell has expressed confidence that the White House will take a back seat willingly.

"I think it's safe to say that we will be looking for, in these non-incumbent races, the most electable candidates possible, and I think the administration will defer to our judgment on Senate races," McConnell said.

A few battles are already shaping up in 2018.

In Ohio, it is unclear whether the GOP establishment will back Mandel, who lost to Brown in 2012.

The Club for Growth is backing Mandel. In 2010, it helped defeat former Sen. Bob Bennett (Utah), one of McConnell's best friends, in a GOP primary.

Rep. Pat Tiberi (R-Ohio), a senior member of the Ways and Means Committee, has amassed $6.3 million in campaign funds and might be seen as a stronger candidate by Washington Republicans.

"We're supporting Josh Mandel in Ohio. I think the establishment would probably prefer Pat Tiberi, but any competent Republican consultant would strongly advise Tiberi not to run," said Andrew Roth, vice president for government affairs at the Club for Growth. "The establishment should like Mandel.

In Missouri, Rep. Ann Wagner (R) appears to be the early establishment favorite to take on Sen. Claire McCaskill (D), but her decision to pull her endorsement of Donald Trump last year could leave her open to attack.

Missouri Attorney General Josh Holly may challenge her, although he just won his office, which makes the chances less likely.

In Wisconsin, the Senate GOP primary has several potential candidates in the mix.

Nicole Schneider, who could fund her own campaign; businessman Eric Hovde; Marine veteran Kevin Nicholson; and state Sen. Leah Vukmir, who was honored last year for her work by the conservative American Legislative Exchange Counsel, could face Sen. Tammy Baldwin (D) in the general election.

The Club for Growth is eyeing the GOP race to take on Sen. Joe Manchin (D-W.Va.).

In Utah, Sen. Orrin Hatch (R) has declared he will run for his eighth term despite promising in 2012 that he would retire next year.

In Arizona, Kelli Ward plans to challenge Sen. Jeff Flake (R), who was one of Trump's biggest critics in the Senate during the 2016 presidential race. Rep. Paul Gosar (R-Ariz.) has criticized Flake for supporting the 2013 comprehensive immigration reform bill but has decided not to challenge him.

In Alabama, Sen. Luther Strange (R), who until recently was the state's attorney general, has to answer questions about former Gov. Robert Bentley's decision to appoint him in the midst of an investigation of the governor. A Republican state representative has complained about the appearance of collusion after Strange asked for the suspension of an impeachment probe before Bentley chose him for the Senate.

On Tuesday, Alabama Gov. Kay Ivey (R) set a special primary for Strange's seat on Aug. 15.

"Just because we haven't seen a Republican Senate incumbent go down in a primary in the last couple cycles doesn't mean Republican primary voters will all of a sudden love the party's leadership," said Kyle Kondik, an analyst at the University of Virginia Center for Politics.